The invention relates to a device for trimming printed products conveyed in an overlapping flow, the device comprising a rotating first knife that operates jointly with a counter-rotating second knife, between which an overlapping flow is conveyed by a conveying device, wherein at least one of the knives is embodied so as to have a plurality of blades distributed along the circumference of the knife and wherein the device is provided with a control unit for controlling the operation of the knives. A rotary cutter of this type is described in the U.S. Pat. No. 3,813,981. The geometric arrangement of the blades along the circumference of one of the two rotating knives makes it possible to prevent the printed products from being displaced during the trimming operation. For that reason, the circumferential speed of the knife provided with the blades must be adapted precisely to the conveying speed of the device for conveying the printed products. To be able to process even thick printed products in an overlapping flow with high production capacity and good trimming quality, the knives of rotary cutters are embodied as shown in the European patent document EP-A-1 510 288. The blades must be re-sharpened regularly because any wear on the knives reduces the trimming quality. This re-sharpening operation is comparatively involved and expensive. A replacement of one or more of the knives furthermore results in a shutdown period, for example ranging from 10 to 30 minutes.